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\title{Reproduction Study of Local Extreme Learning Machines for PDEs}
\author{Prepared by Claude Code Assistant}
\date{October 3, 2025}

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\maketitle

\begin{abstract}
This report consolidates the design, implementation, and evaluation of the locELM Python package, which reproduces the Local Extreme Learning Machine (ELM) method with domain decomposition for solving partial differential equations. Drawing on the accompanying project documentation and experiment logs, we summarize the implemented architecture, review empirical results for one- and two-dimensional Helmholtz benchmarks, and highlight the primary discrepancies that prevented full reproduction of the reference paper. We conclude with targeted recommendations to close the remaining accuracy and performance gaps.
\end{abstract}

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\input{sections/introduction}
\input{sections/project_overview}
\input{sections/implementation}
\input{sections/experiments}
\input{sections/review}
\input{sections/issues}
\input{sections/recommendations}
\input{sections/conclusion}

\end{document}
